Abstract: Argumentation accommodates various rhetorical devices, such as questions, reported speech, and imperatives. These rhetorical tools usually assert argumentatively relevant propositions rather implicitly, so understanding their true meaning is key to understanding certain arguments properly. However, most argument mining systems and computational linguistics research have paid little attention to implicitly asserted propositions in argumentation. In this paper, we examine a wide range of computational methods for extracting propositions that are implicitly asserted in questions, reported speech, and imperatives in argumentation. By evaluating the models on a corpus of 2016 U.S. presidential debates and online commentary, we demonstrate the effectiveness and limitations of the computational models. Our study may inform future research on argument mining and the semantics of these rhetorical devices in argumentation.